First, he was occasionally used as a close approximation of himself — what we might call the "Earth Prime" Jerry Lewis.

Second, he is used in adaptations of films in which he starred. In such cases Lewis serves as the template for the character in the adaptation.

But he is also a character in the regular DC universe — the "Earth-1" Jerry Lewis. In this third type of usage, he had an entirely fictional nephew named Renfew who acted as his sidekick in various misadventures. He also interacted with mainstream DC super-heroes, villains and supporting characters in ways that could not strictly be said to have been parodic, so much as comedic.